scholarly journals Extremality of Disordered Phase of λ-Model on Cayley Trees

Algorithms ◽  
2022 ◽  
Vol 15 (1) ◽  
pp. 18
Author(s):  
Farrukh Mukhamedov
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Gibbs Measure ◽  
Cayley Tree ◽  
Communication Theory ◽  
Arbitrary Order ◽  
Reconstruction Problem ◽  
Free Boundary Conditions ◽  
Cayley Trees ◽  
Disordered Phase

In this paper, we consider the λ-model for an arbitrary-order Cayley tree that has a disordered phase. Such a phase corresponds to a splitting Gibbs measure with free boundary conditions. In communication theory, such a measure appears naturally, and its extremality is related to the solvability of the non-reconstruction problem. In general, the disordered phase is not extreme; hence, it is natural to find a condition for their extremality. In the present paper, we present certain conditions for the extremality of the disordered phase of the λ-model.

scholarly journals Local Well-Posedness for Free Boundary Problem of Viscous Incompressible Magnetohydrodynamics

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 461
Author(s):  
Kenta Oishi ◽  
Yoshihiro Shibata
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Mhd Flow ◽  
Transmission Conditions ◽  
Well Posedness ◽  
Anisotropic Space ◽  
Free Boundary Conditions ◽  
Incompressible Magnetohydrodynamics

In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by a free surface. An electromagnetic field generated by some currents in an external domain keeps an MHD flow in a bounded domain. On the free surface, free boundary conditions for MHD flow and transmission conditions for electromagnetic fields are imposed. We proved the local well-posedness in the general setting of domains from a mathematical point of view. The solutions are obtained in an anisotropic space Hp1((0,T),Hq1)∩Lp((0,T),Hq3) for the velocity field and in an anisotropic space Hp1((0,T),Lq)∩Lp((0,T),Hq2) for the magnetic fields with 2<p<∞, N<q<∞ and 2/p+N/q<1. To prove our main result, we used the Lp-Lq maximal regularity theorem for the Stokes equations with free boundary conditions and for the magnetic field equations with transmission conditions, which have been obtained by Frolova and the second author.

scholarly journals Identification of Corrosion on a Hollow Tube Using Vibration

2014 ◽  
Vol 564 ◽  
pp. 176-181
Author(s):  
S.T. Cheng ◽  
Nawal Aswan Abdul Jalil ◽  
Zamir A. Zulkefli
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Impact Loading ◽  
Structural Damage ◽  
Natural Frequencies ◽  
Localized Corrosion ◽  
Free Boundary Conditions ◽  
The Impact ◽  
Impact Vibration

Vibration based technique have so far been focused on the identification of structural damage. However, not many studies have been conducted on the corrosion identification on pipes. The objective of this paper is to identify corrosion on pipes from vibration measurements. A hollow pipe, 500 mm in length with 63.5 mm in diameter was subjected to impact loading using an impact hammer to identify the natural frequency of the tube in two conditions i) without any corrosion and ii) with an induced localized 40 mm by 40 mm corrosion at the middle of the pipe. The shift of natural frequencies of the structures under free boundary conditions was examined for each node of excitation. The results showed that there is a shift in natural frequency of the pipe, between 3 and 4 Hz near to the corrosion area. It can suggested that that the impact vibration is capable of identifying of localized corrosion on a hollow tube.

Effect of an elastically restrained boundary on SV-wave radiation patterns

1968 ◽  
Vol 58 (2) ◽  
pp. 497-520
Author(s):  
Y. T. Huang
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Elastic Wave ◽  
Solid Earth ◽  
Elastic Constants ◽  
Wave Radiation ◽  
Free Boundary Conditions ◽  
Elastically Restrained

Abstract In the solution of elastic wave propagation equations applied to solid earth, it is customarily assumed that free boundary conditions are satisfied at a surface which is in contact with the atmosphere. Situations which depart from this boundary condition have now been studied for arbitrary combinations of the Lamé elastic constants. The solutions are given for a homogeneous, isotropic half space.

Investigation of the Complex Two Degrees of Freedom Systems for Force Limited Vibration

2004 ◽  
Author(s):  
Andre Cote ◽  
Ramin Sedaghati ◽  
Yvan Soucy
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Simple Approach ◽  
Conservative Estimate ◽  
Two Degrees Of Freedom ◽  
Jet Propulsion ◽  
Fixed Boundary ◽  
Free Boundary Conditions ◽  
Force Data

Force Limited Vibration (FLV) Testing developed at Jet Propulsion Laboratory offers many opportunities to decrease the overtesting problem associated with traditional vibration testing. Among the force limited vibration methods, the complex two degrees of freedom system (TDFS) appears to be the most complete and versatile model which gives reasonably conservative force limits, and does not require extrapolation of interface force data for similar mounting structures and test articles. However there are some limitations to the complex TDFS model. The model is well adapted for nicely separated modes but issues regarding the closely space modes have not been fully addressed in the literature. Also, the complex TDFS model is based on free boundary conditions for the mounting structure, which appear to be natural for many cases such as spacecraft mounted on a launch vehicle. However this is not necessarily true for some other cases such as an electronic component mounted on a spacecraft antenna, which requires fixed boundary conditions. The main objective of this paper is to give greater insights into the complex TDFS method and propose methodologies to overcome its limitations. It is shown that a simple approach can be used to assure conservative estimate of the force limits in situations regarding closely spaced modes. It is also demonstrated that although the complex TDFS method is not perfectly adapted to fixed boundary conditions of the mounting structure, given certain precautions, it still provides good estimates of the force limits.

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